Solve for $x$ and $y$ using elimination. ${-2x+y = -5}$ ${5x-y = 14}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $3x = 9$ $\dfrac{3x}{{3}} = \dfrac{9}{{3}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {-2x+y = -5}\thinspace$ to find $y$ ${-2}{(3)}{ + y = -5}$ $-6+y = -5$ $-6{+6} + y = -5{+6}$ ${y = 1}$ You can also plug ${x = 3}$ into $\thinspace {5x-y = 14}\thinspace$ and get the same answer for $y$ : ${5}{(3)}{ - y = 14}$ ${y = 1}$